A287305 Primes that can be generated by the concatenation in base 5, in descending order, of two consecutive integers read in base 10.

5, 11, 17, 23, 29, 181, 233, 311, 337, 389, 467, 571, 3527, 3779, 4157, 4283, 4409, 4787, 5039, 5417, 5669, 6047, 6173, 6299, 6551, 6803, 7307, 7433, 7559, 7937, 8693, 8819, 9323, 10079, 10331, 10457, 10709, 11087, 11213, 11717, 11969, 12347, 12473, 13103, 13229

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Example

1 and 2 in base 5 are 1 and 2 and concat(2,1) = 21 in base 10 is 11;
6 and 7 in base 5 are 11 and 12 and concat(1211) = 1211 in base 10 is 181.

Maple

with(numtheory): P:= proc(q, h) local a, b, c, d, k, n; if q=0 then 5 else a:=convert(q+1, base, h); b:=convert(q, base, h); c:=[op(a), op(b)]; d:=0; for k from nops(c) by -1 to 1 do d:=h*d+c[k]; od; if isprime(d) then d; fi; fi; end: seq(P(i, 5), i=0..1000);

Mathematica

With[{b = 5}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Reverse /@ Partition[Range[0, 108], 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)

Crossrefs

Cf. A000040, A052089.

Sequence in context: A335070 A354748 A194384 * A189938 A184525 A252596

Adjacent sequences: A287302 A287303 A287304 * A287306 A287307 A287308

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 23 2017

Status

approved